St. Petersburg Mathematical Journal, 16. ciltAmerican Mathematical Society, 2005 |
Kitabın içinden
27 sonuçtan 1-3 arası sonuçlar
Sayfa 403
... harmonic if and only if the deformation tensor T = ▽ − ▽ of ▽ under the mapping f is a section of the tensor vector bundle TM & SZM . - 1.2 . Examples of harmonic diffeomorphisms f : ( M , g ) → ( M , ğ ) . 1.2.1 . Conformal ...
... harmonic if and only if the deformation tensor T = ▽ − ▽ of ▽ under the mapping f is a section of the tensor vector bundle TM & SZM . - 1.2 . Examples of harmonic diffeomorphisms f : ( M , g ) → ( M , ğ ) . 1.2.1 . Conformal ...
Sayfa 410
... harmonic transformations . Applying formulas ( 3.1 ) , we see that έ is an infinitesimal harmonic transformation if satisfies the equations ( 3.3 ) g13 ( L¿Ãk ; ) == 0 . Theorem 3.1 . A vector field E CTM is an infinitesimal harmonic ...
... harmonic transformations . Applying formulas ( 3.1 ) , we see that έ is an infinitesimal harmonic transformation if satisfies the equations ( 3.3 ) g13 ( L¿Ãk ; ) == 0 . Theorem 3.1 . A vector field E CTM is an infinitesimal harmonic ...
Sayfa 411
... harmonic transformations . Theorem 3.4 . An infinitesimal harmonic transformation & of a Riemannian manifold ( M , g ) is isometric if M is compact and the field is solenoidal . Proof . We recall that the relations Ac * = 2R§1 and V ̧§1 ...
... harmonic transformations . Theorem 3.4 . An infinitesimal harmonic transformation & of a Riemannian manifold ( M , g ) is isometric if M is compact and the field is solenoidal . Proof . We recall that the relations Ac * = 2R§1 and V ̧§1 ...
İçindekiler
ISOMETRIC EMBEDDINGS OF FINITEDIMENSIONAL pSPACES | 11 |
OVER THE QUATERNIONS | 104 |
1 Introduction | 117 |
Telif Hakkı | |
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analytic approximation assume asymptotic Birman BKN-equation bounded C(zIm coefficients cohomology classes compatible components constant corresponding defined denote diffeomorphism Dirac operator domain edge eigenvalues embedding English transl estimate Euler characteristic exists finite formula geodesic graph graph-manifold harmonic Hilbert space holomorphic implies inequality integral invertible isometric K₁ kernel Lemma length function linear Math matrix matrix-valued function maximal blocks meromorphic monodromy nonzero norm NPC-solution obtain oriented Painlevé equations pair paper polynomial positive potential problem proof of Theorem properties Proposition prove rational refinable function relation representation respect result Riemann-Hilbert Riemann-Hilbert problem Riemannian manifold S₁ satisfies Schrödinger operator Seifert fibered space self-affine selfadjoint selfadjoint operators singular Sobolev Sobolev spaces solution spectrum Subsection subspace supp Suppose symmetric Theorem Theorem 3.1 theory torus vector vertex vertices zero